Enduring Understandings and Essential Questions for Performance Task
Enduring Understandings
Students understand that real-world situations can be modeled using mathematical functions.
Students understand that these real-world situations, and the corresponding, can also be represented numerically - with a table of values - and graphically
Students understand the difference between average velocity and instantaneous velocity
Students understand the concept of average and instantaneous rate of change, and how the derivative can be used to find the instantaneous rate of change of one variable with respect to another.
Students understand the connection between the tangent line to a function, the derivative, and the rate of change of one variable with respect to another
Students understand the connection between this graphical representation of a tangent line and the algebraic representation of the derivative function
Essential Questions
How can a function be used to model the position, velocity, or acceleration of a real-world object?
How can this function be shown graphically and numerically, and what does this tell us about the real-world object it is modeling?
How can we use the ideas of slopes, secant lines, and tangent lines to relate the position of an object as a function of time to its average or instantaneous velocity?
How does the idea of the derivative as a rate of change help us to understand the relationships between position, velocity, and acceleration?
How can this idea of rate of change, and the derivative as the slope of the tangent line to a function, be applied to other situations in which we want to find the rate of change of one variable with respect to another?
How can the functional representation of the derivative and the graphical representation of the tangent line enhance our understanding of the problem we are studying?
Enduring Understandings
Essential Questions